[email protected] · 2004. 7. 7. · the standard model a. pich - sant feliu 2004 antonio pich...

The Standard Model A. Pich - Sant Feliu 2004

Antonio Pich

IFIC, CSIC – Univ. Valencia

[email protected]


§§ Fermion MassesFermion Masses

§§ Fermion GenerationsFermion Generations

§§ Quark MixingQuark Mixing

§§ Lepton MixingLepton Mixing

§§ Standard Model ParametersStandard Model Parameters

§§ CPCP ViolationViolation


Quarks Leptons Bosons

photon

gluon

Higgs

up down electron neutrino e

charm strange muon neutrino µ

top beauty tau neutrino τ

e

µ

τ

ZZ00 WW ±±


Fermion Fermion Masses Masses areare

NewNew Free Free ParametersParameters

Couplings Couplings FixedFixed::f

H f f

mg

v=

fmv

f

f

H

{ }1v udY q q u ud d lm qH

q m q q m l l + = − + +

L

SSBSSB

( ) ( ) ( ) v, , , ,

2ud

d u lq q lm m m c c c = −

FERMION MASSESSFERMION MASSESSScalarScalar Fermion Couplings allowed Fermion Couplings allowed by by Gauge Gauge SymmetrySymmetry

0

0 0

( ) ( )† ( )

( ) ( )†( ) ( )

()

)(( , ) ( ) ( ) ( , ) h.c.u L R u R L Rd d

u ll

dY c c cq q q q v l l

φ φ φφ φ φ

+ +

+

−

= + + +

L


FERMION GENERATIONSFERMION GENERATIONS

( ) ( )( ) (0)† ( )

(0) ( )† (0)( ) ( ) ( ), , h.c.Y j j j jk R k R k RL L

j k

d u ljk jk j ku d d u v l lc c c

φ φ φφ φ φ

+ +

+

′ ′ ′ ′

− ′ ′ ′= + + +

∑Ll

{ }1v

h.c.Y L R L R L Rud ld d u u l lH ′ ′ ′ ′ ′ ′ ′ ′ ′= − ⋅ ⋅ + ⋅ ⋅ + ⋅+ ⋅ +

M M MlL

SSBSSB

Arbitrary Arbitrary NonNon--Diagonal Diagonal Complex Complex Mass Mass MatricesMatrices( ) ( ) ( ) v, ,

2, ,d u l

ud l jk jk jkjkc c c ′ ′ ′ = − M M M

Masses Masses are are the only differencethe only differenceGN 3= Identical Identical CopiesCopies

WHY ?WHY ?0

1

Q

Q

=

= −

2 3

1 3

Q

Q

= +

= −j j

j j

v ul d

′ ′ ′ ′

( )G1,...,Nj =


DIAGONALIZATION OF MASS MATRICESDIAGONALIZATION OF MASS MATRICES†

d

†u

†

Sd d d d d d

u u u u u u

l l l l l l l

′ = ⋅ = ⋅ ⋅ ⋅

′ = ⋅ = ⋅ ⋅ ⋅

′ = ⋅ = ⋅ ⋅ ⋅

M H U S S U

M H U S U

M H U S S U

dMMM

†f f

† †f f f f

† †f f f f

1

1

=

⋅ = ⋅ =

⋅ = ⋅ =

H H

U U U U

S S S S

( ) { }d d + u1 u +vY d u llH l= − ⋅ ⋅ ⋅+ ⋅ ⋅ ⋅lL M M M

diag ( , , ) ; diag ( , , ) dia , ,; g ( )d lu c t s ed bu m m m m m m m m mµ τ= = =M M M

L

R

d d ; u u ;

d d ; u u ;d L L u L L l L

d d R R u u R R l l R

l l

l l

′ ′ ′≡ ⋅ ≡ ⋅ ≡ ⋅

′ ′ ′≡ ⋅ ⋅ ≡ ⋅ ⋅ ≡ ⋅ ⋅

S S S

S U S U S U

Mass EigenstatesMass Eigenstates

Weak EigenstatesWeak Eigenstates≠

N C N C′ =L Lf f f f ; f f f fL L L L R R R R′ ′ ′ ′= =

QUARK MIXINGQUARK MIXING

†u d u d ; u dL L L L⋅′ ′ = ⋅ ≡ ⋅S SV V CC CC′ ≠L L

µ


[ ]f f 5Nf

C f f2 sin cos

v aW W

Z Ze

µµγ

θ θγ−= ∑L

Flavour Conserving Flavour Conserving Neutral Neutral CurrentsCurrents

u c t

d s b

Flavour Flavour Changing Charged Changing Charged CurrentsCurrents

( ) ( )i5 5C C†

iji j

j1 1 h.c.

2 2 ll

gu d vW lµ

µ µγ γ γ γ

= − + − + ∑ ∑VL


( )i 5 j

i

( )CC

jij

† (1 ) h.c.2 2

ll Wg

lL µµ ν γ γ= − +∑ Vl

Separate Separate Lepton Lepton Number Number ConservationConservationR( )νMinimal SM without

i( )

ijj

llν ν≡ V

( ) †5CC (1 ) h.c.

2 2l

ll

lg

L W µµ ν γ γ− += ∑ll IFIF i

m 0ν =

( Co, n, served )eeL L L LL L µµ ττ + +

ll IFIFi

iR exist and m 0νν ≠

BUTBUT 11 7Br ( ) 1.2 10 Br ( ) 3.1 10eµ γ τ µ γ− −→ < × → < ×;(90 % CL)


W

jdiu

e−

eν

ijV

Measurements of VMeasurements of Vijij

j i

2

ij( )ed u e ν−Γ → ∝ V

We measure decays of hadrons (no free quarks)

Important QCD Uncertainties


*

0.9739 0.0005

0.2196 0.0026

0.224 0.016

0.9740 0.0005

0.9731 0.0015

1.04 0.16

0.97 0.11

0.0

0.0421 0.0022

0.0414 0.0009

0.0

Nuclear

415 0.00

dec

1

ay

0

ud

u

l

l

s

cd

cs

cb

ub

e

e

e

n p e v

K e v

v d c X

D K e v

W c

V

V

V

V

V

V

s

B D l v

b c l v

β

π

−

−

+

+

→

→

→

→

→

→

→

±

±

±

±

±

±

±

±

±

±

0.160.12

033 0.0005

0.0041 0

0.

.0

0036 0.0005

006

0 7 /.9

l

l

B l v

b u l v

t bW qW

ρ

+−

→

±

→

±

± →

2 22 0.9967 0.0021usud ubV V V+ + = ± ( )2 2(LEP)2.027 0.025u j c j

jV V+ = ±∑

CKM entry Value Sourcei jV

2

q t qtb VV ∑


QUARK MIXING MATRIXQUARK MIXING MATRIX

ll Unitary MatrixUnitary Matrix:: parametersparametersG GN N× 2GN

ll arbitrary phasesarbitrary phases::G2 1N −

jii i j j;e eiiu u d dθφ→ → j i )

ij j(

iei θ φ−→V V

ijV

( )G G1

12

N N −

Physical ParametersPhysical Parameters::

Moduli Moduli ;; phasesphasesG G1 ( 1) ( 2)2

N N− −


UnitarityUnitarity:: † †⋅ = ⋅ =V V V V 1

fN = 2 : 1 angle, 0 phasesll

C C

C C

cos sinsin cos

θ θθ θ

= −

V No CP

( )13

13 13

13 13

2 312 13 12 13 13

2 2 412 23 12 23 13 12 23 12 23 13 23 13

3 212 23 12 23 13 12 23 12 23 13 23 13

1 /2 ( )1 /2

(1 ) 1

i

i i

i i

c c s c s As c c s s c c s s s s c A

s s c c s c s s c s c c A A

e ie ee e i

δ

δ δ

δ δ

λ λ λ η

η

ρλ λ λ λ

λ ρ λ

− − − − − − ≈ − − + − − − − − −

O

i j ij ij ij (i,j 1, 2, 3)cos ; sinc sθ θ =≡ ≡ 2 2Csin 0.223 ; 0.82 ; 0.41Aλ θ ρ η≈ ≈ ≈ + ≈

(CKM)3fN = : 3 angles, 1 phasell

13 0)0 (ηδ ≠≠ CP


Standard Standard Model Model ParametersParameters

QCD:QCD:

EW EW Gauge Gauge / / Scalar Scalar Sector:Sector:

( )S ZMα 11

442 , , ,, , , , , , F ZW H HWg g h M M MM Gµ α αθ⇔ ⇔′

1313Yukawa Yukawa Sector:Sector:

1 2 3

, ,

, ,

, ,

, , ,

e

sd b

u c t

m m m

m m m

m m m

µ τ

θ θ θ δ

18 Free 18 Free ParametersParameters (+ Neutrino (+ Neutrino Masses Masses / / Mixings Mixings ?)?)

TOO MANY !TOO MANY !


l C , P : Violated maximally in weak interactions

l CP : Symmetry of nearly all observed phenomena

l Slight (~ 0.2 %) CP in decays (1964)

l Sizeable CP in decays (2001)

l Huge Matter Antimatter Asymmetryin our Universe Baryogenesis

§ Complex Phases

§ Interferences

Thus, CP requires:

CPT Theorem: TCP

0K0B


Meson – Antimeson Mixing

0B 0B

0B

0B

f2 Interfering Amplitudes

0 0

0 0

( / ) ( / )0

( / ) ( / )S S

S S

B J K B J KB J K B J K

ψ ψψ ψ

Γ → − Γ →≠

Γ → + Γ →

SignalCP

BABAR


* * * 0ud ub cd cb td tbV V V V V V+ + =

* *ud ub cd cbV V V V * *

td tb cd cbV V V V


Complex Complex phases phases in in Yukawa Yukawa couplings couplings onlyonly::

The The CKM CKM matrix matrix VVij ij is the only is the only source of source of CPCP

( ) ( )jk j

( ) (0)†

j j L k R kR(0) ( )†j k

k( , ) h.c.Yd uL d d uc cu

φ φφ φ

+

+

′ ′ ′ ′= + + −

∑

(0) v / 2φ = SSBSSB

{ }( ) (jL k R jj jkL kR

)k

v1 h.cv

.2

uY

dcd d uL H uc ′ ′ ′ ′= − + + +

( )jkqc diagonalization

{ }jjjL jR jL jR

†CC i 5 j

i jij

1 h.c.

(1 ) h.c.2 2

vY udL d d u u

gL W u

m mH

dµµ γ γ

= − + + +

= − +∑ V

The Standard Model A. Pich - Sant Feliu 2004The Standard Model A. Pich - Sant Feliu 2004


e µν ν↔

Neutrino Neutrino OscillationsOscillations

µ τν ν↔

CPRν ?,

NEW PHYSICSNEW PHYSICS

Lepton Mixing

M.C. González-García , C. Peña-Garay


THE STANDARD THEORY OF THE STANDARD THEORY OF FUNDAMENTAL INTERACTIONSFUNDAMENTAL INTERACTIONS

( ) ( ) ( )C L YSU 3 SU 2 U 1⊗ ⊗

Electroweak Electroweak + + Strong Strong ForcesForces

l Gauge Symmetry Dynamics

l 3 Gauge Parameters:

l All Known Experimental Facts Explained

l Problem with Mass Scales / Mixings:

( )2 , ,Z Ws Mα α θ

- 15 Additional Parameters

- Why 3 Families ?

- Why Left ≠ Right ?

- Why ?

- Does the Higgs Exist ?

- Flavour Mixing- CP Violation

- Neutrino Masses / Oscillations

Ztm M>


WANTEDWANTED

HiggsHiggsGREAT REWARDGREAT REWARD

STOCKHOLM


WANTEDWANTED

HiggsHiggsGREAT REWARDGREAT REWARD

STOCKHOLM

e

µ

τ

[email protected] · 2004. 7. 7. · the standard model a. pich - sant feliu 2004 antonio pich...

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